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DOI: 10.1002/anie.201310637
Giant Diamagnetism
Anomalous Diamagnetic Susceptibility in 13-Atom Platinum
Nanocluster Superatoms**
Emil Roduner,* Christopher Jensen, Joris van Slageren, Rainer A. Rakoczy, Oliver Larlus, and
Michael Hunger
Abstract: We are used to being able to predict diamagnetic
susceptibilities cD to a good approximation in atomic increments since there is normally little dependence on the chemical
environment. Surprisingly, we find from SQUID magnetization measurements that the cD per Pt atom of zeolite-supported
Pt13 nanoclusters exceeds that of Pt2+ ions by a factor of 37–50.
The observation verifies an earlier theoretical prediction. The
phenomenon can be understood nearly quantitatively on the
basis of a simple expression for diamagnetic susceptibility and
the superatom nature of the 13-atom near-spherical cluster. The
two main contributions come from ring currents in the
delocalized hydride shell and from cluster molecular orbitals
hosting the Pt 5d and Pt 6s electrons.
N
anosize particles of metallic elements have attracted great
attention because their properties often deviate markedly
from those of the bulk metal. For example, micro- and
nanosize platinum particles are reported to become superconducting,[1–3] whereas bulk Pt does not. There are predictions that metal clusters with 102–103 free carriers may
become superconducting.[4] Furthermore, at low temperature,
Pt nanoparticles and clusters show pronounced superparamagnetism,[5–7] whereas bulk Pt has a small positive magnetic
susceptibility arising from Pauli paramagnetism which is
slightly temperature dependent.[8] Other work predicts
a greatly enhanced diamagnetism in metal clusters,[9, 10] but
there has been no experimental verification of this. Diamagnetism is an important indicator of superconductivity as well,
which raises the interest in this property for small clusters
even further. However, since the London penetration depth
of superconductors is normally on the order of 100 nm it
[*] Prof. E. Roduner, Dr. C. Jensen, Prof. J. van Slageren
Institute of Physical Chemistry, University of Stuttgart
70563 Stuttgart (Germany)
E-mail: [email protected]
Dr. R. A. Rakoczy, Dr. O. Larlus
Clariant Produkte Deutschland GmbH
Lenbachplatz 6, 80333 Munich (Germany)
Prof. M. Hunger
Institute of Technical Chemistry, University of Stuttgart
70563 Stuttgart (Germany)
Prof. E. Roduner
University of Pretoria
0002 Pretoria (Republic of South Africa)
[**] We thank Hermann Stoll for useful discussions and the 1st Physical
Institute of the University of Stuttgart for letting us use their SQUID
magnetometer.
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201310637.
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should not be expected to find an ideal diamagnetism with full
exclusion of the magnetic field for objects of less than 1 nm
diameter. In addition, since magnetic properties reflect the
wave function they are of general interest in physics as well as
in chemistry.
We have previously demonstrated that monodisperse
icosahedral or cuboctahedral platinum nanoclusters with
13 2 atoms can be prepared supported within the porous
structure of NaY zeolite.[6] Although they are all of the same
size they exist in three different magnetic states: 15–20 % in
a high-spin state with magnetic moments of m = 3.7 0.4 and
3.0 0.4 mB for [Pt13] and [Pt13Hm], respectively, a very small
fraction, less than 1 %, contributes to the spin-1=2 EPR signal,
and the rest is diamagnetic.[7] The coexistence of different
electronic states of the same cluster may be rationalized by
different local environments, such as the presence of different
numbers of zeolite framework Al atoms or extra-framework
cations, Na+ or K+, in close proximity to the cluster, and the
extent of hydrogen coverage will also play a role.
Herein we resume the subject of magnetism with these
clusters using a specially synthesized iron-free L zeolite
(Supporting Information) to avoid any interference of iron
and ambiguities in the interpretation of the data. The
potassium form of the zeolite was exchanged using a 3 mm
solution of [Pt(NH3)4]Cl2. The product was washed, dried,
and then calcined in a flux of O2 while the sample was heated
at a rate of 0.5 K min1, and keeping the final temperature
(623 K) for 5 h. Reduction was then performed in flowing H2
at a heating rate of 4 K min1 and keeping the sample at 503 K
for 1 h. The structure of the obtained zeolite sample was
characterized by X-ray diffraction and solid-state NMR
specrtoscopy(see Supporting Information, Figure S1 and
S2), while the investigation of the Pt clusters was performed
by extended X-ray absorption fine structure (EXAFS)[6, 11]
and EPR spectroscopy. Details about the experimental
procedure which are crucial for formation of clusters of
a defined size are found elsewhere.[12, 13] The extent of H2 or D2
coverage was determined by sequential addition of calibrated
hydrogen aliquots and monitoring the pressure.[11]
The EPR spectrum of a [Pt13DX] cluster shows a multiplet
spectrum with a regular splitting (see Figure S3). The pattern
fits well the hyperfine interaction of the unpaired electron
with 12 equivalent Pt nuclei in natural isotopic abundance
and suggests a superatom structure (Supporting Information).
The resolved multiplet is clear evidence for a molecular rather
than metallic character of the cluster.
Magnetization measurements were performed with
a [Pt13H38] and a [Pt13H18] sample using a superconducting
quantum interference device (SQUID, quantum design
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MPMXL7). Paramagnetism was discussed in detail in
Ref. [12]. In short, Curie behavior with a Curie–Weiss
constant q = 0 was observed in a temperature range of 20–
70 K. A magnetic moment of 0.236(2) mB per Pt atom was
obtained for both samples,[13] corresponding to J 1.5 for the
13-atom cluster or three unpaired electrons if the moment is
due to electron moments only. These values oscillate significantly with the amount of chemisorbed hydrogen, and they
show some development with time.[12, 13] Previous XMCD (Xray magnetic circular dichroism) measurements of two similar
samples with not quantitatively known hydrogen coverage
revealed a ratio of orbital to spin magnetic moments, mL/mS of
0.30(2), and thus to an orbital angular momentum contribution to paramagnetism of approximately 23 %, significantly
less than for bulk Pt (28 %).[7]
The magnetization saturation curves shown in Figure 1 A
reveal the paramagnetic nature of the samples owing to
a fraction of high-spin clusters at low temperature. All
magnetizations are corrected for the contribution of the
plain zeolite. At room temperature and fields greater than
0.2 T, however, the magnetizations turn negative, scaling
linearly with field, so the behavior is clearly dominated by
diamagnetism.
explanation of the subtraction of the zeolite contribution.
The slopes of the resulting straight lines in Figure 1 B are the
molar magnetic susceptibilities, in cgs units, given by cD =
441(1) 106 cm3 and cD = 602(4) 106 cm3 per mol Pt
atoms of [Pt13H18] and [Pt13H38], respectively. The latter
sample is saturated with hydrogen at a pressure of
540 mbar.[11] These values are spectacular, larger by as much
as a factor of 37–50 compared with expected values for nonmetallic diamagnetic Pt [cD(Pt) 2cD(PtCl2)cD(PtCl4) =
11 106 cm3 mol1;
or
cD(Pt) cD(PtCl2)cD(Cl2) =
13.5 106 cm3 mol1].[16]
All Pt species contribute to the diamagnetic susceptibility.
The origin of this property is normally attributed to ring
currents on atoms which lead to a magnetic moment that is
antiparallel to the external magnetic field (Figure 2). It is
Figure 2. The mechanism of diamagnetism is ascribed to magneticfield-induced ring currents which are localized on the atoms and lead
to a small magnetic moment that scales with the square of the radius
and is antiparallel to the external magnetic field (left). Owing to the
superatom nature of clusters, the ring current operates in the
delocalized valence orbitals (right). The strongly enhanced diamagnetism is due to the cluster radius and the large number of electrons
involved.
Figure 1. SQUID magnetization measurements obtained with 5.5 wt. %
Pt supported on iron-free KL-zeolite for A) [Pt13H18] (full dots) and
[Pt13H38] (empty squares) and B) for 300 K on an expanded scale. The
magnetization of the same amount of zeolite in the absence of Pt was
subtracted. The numbers are given per mol Pt atoms.
Above 40 K, the EPR signal diminishes much more
quickly than predicted by the Curie law, indicating that
a chemical equilibrium is also involved.[14] If this is also true
for the high-spin state then it is not surprising that nearly no
influence of the paramagnetic fraction is observed at 300 K.
Elsewhere, it was demonstrated for the 13-atom clusters
Mn@Sn12 that excitation of Jahn–Teller active vibrations has
a pronounced effect on the spin structure and causes rapid
transitions between states.[15] Evidence for the excitation of
vibrations at low frequencies as expected for the heavy-atom
Pt clusters comes from the relaxation rate of the [Pt13DX] EPR
signal which increases with the square of temperature.[14]
The raw data of the field-dependent magnetization
measurements are given in Figure S4, together with an
Angew. Chem. Int. Ed. 2014, 53, 4318 –4321
analogous to the mechanism which is responsible for the large
diamagnetic screening in the proton NMR spectrum of
benzene. For a closed-shell cluster consisting of N atoms
electron-spin paramagnetism and orbital diamagnetism
vanish, and the dimensionless volume susceptibility c is
given to first order in SI units by Equation (1)[17]
c¼
e2 m0 N X 2 ri
6me V i
ð1Þ
where m0 is the vacuum permeability, and e and me are the
electron charge and mass, respectively. V is the atomic
volume,
0.0152 nm3 based on the bulk density of Pt, and
2
ri is the mean square electron distance of the i-th electron
from the center. To convert Equation (1) into molar susceptibilities cm, c has to be multiplied by the molar volume,
9.09 cm3 mol1, and to convert into the more conventional cgs
units cD in which all values
are quoted herein, it has to be
divided by 4p. In atoms, ri2 is on the order of a02, where a0 is
the Bohr radius. The ground-state electron configuration of Pt
is [Xe]4f145d96s1.
In the superatom picture it will be the delocalized cluster
molecular orbitals which determine diamagnetism. These
provide larger radii for the ring currents (see Figure 2), but it
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Table 1: Diamagnetic susceptibility cD of [Pt13Hx] clusters in units of 106 cm3 per mol Pt atoms.
Sample
[Pt13H38]
[Pt13H18]
[Pt13]
(i) [Xe]4f14 core[b]
Calculated contribution (number of electrons)
(ii) Hydride shell[c]
(iii) 5d6s shell[a]
(iv) 5d6s shell[a]
Overall Pt13 cluster
Pt4 tetrahedra
sum
12
12
12
313 (76/13)
148 (36/13)
0
522
399
293
135 ((120-38)/13)
167 ((120-18)/13)
200 (120/13)
Experimental value
62 ((40-38·3/12)/4)
72 ((40-18·3/12)/4)
81 (40/4)
602(4)
441(1)
Not measured
[a] Ten 5d and 6s electrons for each of the 12 surface Pt atoms, diminished by the number of electrons which are involved in the PtH bonds, (i)–(iv)
refer to the description of the contributions in the main text. cD is given per atom of the 13-atom cluster. [b] Approximate experimental value for Pt2+,
see text. The number should be diminished slightly through the atomic contribution of the remaining eight d electrons which are part of the 5d6s
superatom shell. [c] Two electrons per PtH bond.
appears nevertheless challenging to explain the experimental
enhancement by a factor 37–50, depending on hydrogen
coverage. In addition to the conventional atomic values (i, see
Table 1) we discuss three possible further contributions:
ii) Surprisingly, it was found necessary to involve the shell of
chemisorbed hydrogen atoms. The 1s atomic orbital of H is
energetically significantly lower than the 5d orbital of Pt to
which it is bound. The PtH bonding orbital will thus also be
of low energy, about 5 eV below the Fermi level, making H
partly hydride-like (the antibonding orbital is slightly above
the Fermi level[18]). In DFT quantum chemical calculations
the bridge-bonded site along the cluster edge was predicted
the most stable, but this is without any corrections for zeropoint vibrational motion, and the difference to the on-top Pt
and the threefold hole sites is not large.[14, 19] The H–H
distance of saturated Pt clusters amounts to about 0.22 nm or
4.7 a0.[19] At this distance there is considerable overlap of the
H 1s electrons, in particular in the hydridic state, which
justifies regarding the Pt bound hydrides as a set of doubly
occupied delocalized cluster molecular orbitals.[19] Approximating the radial distance of this shell from the cluster center
by the sum of the PtPt and the PtH bond lengths (0.277 nm
+ 0.158 nm = 0.435 nm) we arrive at a contribution to cD of
53.5 106 cm3 per mol hydride electrons. Per Pt atom this
yields cD = 148 106 cm3 for [Pt13H18], and 313 106 cm3
for [Pt13H38]. iii) The next contribution is due to the delocalized Pt valence electrons. ri is the positive cluster core radius,
which is taken in this case as the bulk Pt interatomic distance,
d = 0.277 nm.[20] On this basis we obtain cD = 21.6 106 cm3
per mol valence electrons. iv) Induced ring currents cannot
only extend over the entire cluster, but also over smaller
building blocks. A 13-atom cuboctahedron consists of one
central atom surrounded by six atoms in one plane. Three
adatoms are found on top and three more below this plane.
This structure can be thought of as being composed of six
edge-sharing Pt4 tetrahedra, three pointing up from the
central plane and three down. The four atoms sit on a sphere
with a radius R = 0.25·6 = d, leading to an increment cD =
8.1 106 cm3 per mol valence electrons.
There are also 14 4f electrons per atom. If they were
delocalized over the cluster this would lead to a contribution
of the required magnitude. However, they are energetically
lower by 73 eV than the 5d and 6s electrons and have an
atomic hr2i expectation value of only 0.3 a02, an order of
magnitude less than the 4d electrons.[21] This situation leaves
them little probability of overlap and delocalization, so they
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will contribute only to the atomic core values. Indeed, they
are not normally regarded as valence orbitals.
The four contributions to cm are collected in Table 1.
Contribution (iv) of the Pt4 tetrahedra appears to be minor
but non-negligible. Furthermore, for icosahedra in place of
cuboctahedra the building blocks would have to be constructed differently. The added contributions account for
87 % of the experimental value for [Pt13H38] and to 90 % for
[Pt13H18]. The predicted values are somewhat low, but
considering the extensive and debatable approximations in
the model the results are still considered to be in perhaps very
good qualitative agreement with experiment. The advantage
of the model is that it provides insight into the possible
mechanism of diamagnetism in nanoparticles. Detailed quantum chemical predictions would be highly desirable, but such
calculations seem currently to be out of range for a heavy
element such as Pt, for which relativistic effects are crucial.
The SQUID results represent an ensemble average over
all the Pt species, but potential size and shape inhomogeneities are expected to play a limited role for the diamagnetism.
The agreement between theoretical model and experimental
result suggests that the observed phenomenon has nothing to
do with a superconducting transition, even though the clusters
have 102–103 delocalized electrons.[4] Since the EPR multiplet
confirms that the clusters are non-metallic this also excludes
other origins, such as a negative Knight shift. Instead, we
believe that this is the first experimental observation of the
predicted anomalously enhanced diamagnetic susceptibility
in a well-defined finite-size delocalized system.
A superatom shell-type electronic structure has also been
predicted in density functional calculations for Pt13 clusters
which did not include any chemisorbed hydrogen atoms.[22]
The present essentially quantitative agreement strongly
supports that the superatom concept provides a useful
description for understanding small spherical clusters. Both,
this concept and the strongly enhanced diamagnetism are
characteristic and unique for nanomaterials with delocalized
electron systems.
It would be interesting to investigate the transition to bulk
behavior which has been predicted to occur at a nanoparticle
size with a radius on the order of 10 mm.[10]
Received: December 8, 2013
Revised: January 27, 2014
Published online: March 18, 2014
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.
Keywords: diamagnetism · EPR spectroscopy ·
platinum clusters · superatoms
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